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For reasons best known to their lawyers, Red Hat have chosen to hobble their implementation of OpenSSL. According to a releated bug, possible patent issues have led them to remove a large number of the elliptic curve parametrisations, as you can see by comparing the curves supported on Fedora 25:

flypig@Owen:~$ openssl ecparam -list_curves
secp112r1 : SECG/WTLS curve over a 112 bit prime field
secp112r2 : SECG curve over a 112 bit prime field
secp128r1 : SECG curve over a 128 bit prime field
secp128r2 : SECG curve over a 128 bit prime field
secp160k1 : SECG curve over a 160 bit prime field
secp160r1 : SECG curve over a 160 bit prime field
secp160r2 : SECG/WTLS curve over a 160 bit prime field
secp192k1 : SECG curve over a 192 bit prime field
secp224k1 : SECG curve over a 224 bit prime field
secp224r1 : NIST/SECG curve over a 224 bit prime field
secp256k1 : SECG curve over a 256 bit prime field
secp384r1 : NIST/SECG curve over a 384 bit prime field
secp521r1 : NIST/SECG curve over a 521 bit prime field
prime192v1: NIST/X9.62/SECG curve over a 192 bit prime field
prime192v2: X9.62 curve over a 192 bit prime field
prime192v3: X9.62 curve over a 192 bit prime field
prime239v1: X9.62 curve over a 239 bit prime field
prime239v2: X9.62 curve over a 239 bit prime field
prime239v3: X9.62 curve over a 239 bit prime field
prime256v1: X9.62/SECG curve over a 256 bit prime field
sect113r1 : SECG curve over a 113 bit binary field
sect113r2 : SECG curve over a 113 bit binary field
sect131r1 : SECG/WTLS curve over a 131 bit binary field
sect131r2 : SECG curve over a 131 bit binary field
sect163k1 : NIST/SECG/WTLS curve over a 163 bit binary field
sect163r1 : SECG curve over a 163 bit binary field
sect163r2 : NIST/SECG curve over a 163 bit binary field
sect193r1 : SECG curve over a 193 bit binary field
sect193r2 : SECG curve over a 193 bit binary field
sect233k1 : NIST/SECG/WTLS curve over a 233 bit binary field
sect233r1 : NIST/SECG/WTLS curve over a 233 bit binary field
sect239k1 : SECG curve over a 239 bit binary field
sect283k1 : NIST/SECG curve over a 283 bit binary field
sect283r1 : NIST/SECG curve over a 283 bit binary field
sect409k1 : NIST/SECG curve over a 409 bit binary field
sect409r1 : NIST/SECG curve over a 409 bit binary field
sect571k1 : NIST/SECG curve over a 571 bit binary field
sect571r1 : NIST/SECG curve over a 571 bit binary field
c2pnb163v1: X9.62 curve over a 163 bit binary field
c2pnb163v2: X9.62 curve over a 163 bit binary field
c2pnb163v3: X9.62 curve over a 163 bit binary field
c2pnb176v1: X9.62 curve over a 176 bit binary field
c2tnb191v1: X9.62 curve over a 191 bit binary field
c2tnb191v2: X9.62 curve over a 191 bit binary field
c2tnb191v3: X9.62 curve over a 191 bit binary field
c2pnb208w1: X9.62 curve over a 208 bit binary field
c2tnb239v1: X9.62 curve over a 239 bit binary field
c2tnb239v2: X9.62 curve over a 239 bit binary field
c2tnb239v3: X9.62 curve over a 239 bit binary field
c2pnb272w1: X9.62 curve over a 272 bit binary field
c2pnb304w1: X9.62 curve over a 304 bit binary field
c2tnb359v1: X9.62 curve over a 359 bit binary field
c2pnb368w1: X9.62 curve over a 368 bit binary field
c2tnb431r1: X9.62 curve over a 431 bit binary field
wap-wsg-idm-ecid-wtls1: WTLS curve over a 113 bit binary field
wap-wsg-idm-ecid-wtls3: NIST/SECG/WTLS curve over a 163 bit binary field
wap-wsg-idm-ecid-wtls4: SECG curve over a 113 bit binary field
wap-wsg-idm-ecid-wtls5: X9.62 curve over a 163 bit binary field
wap-wsg-idm-ecid-wtls6: SECG/WTLS curve over a 112 bit prime field
wap-wsg-idm-ecid-wtls7: SECG/WTLS curve over a 160 bit prime field
wap-wsg-idm-ecid-wtls8: WTLS curve over a 112 bit prime field
wap-wsg-idm-ecid-wtls9: WTLS curve over a 160 bit prime field
wap-wsg-idm-ecid-wtls10: NIST/SECG/WTLS curve over a 233 bit binary field
wap-wsg-idm-ecid-wtls11: NIST/SECG/WTLS curve over a 233 bit binary field
wap-wsg-idm-ecid-wtls12: WTLS curvs over a 224 bit prime field
Oakley-EC2N-3:
IPSec/IKE/Oakley curve #3 over a 155 bit binary field.
Not suitable for ECDSA.
Questionable extension field!
Oakley-EC2N-4:
IPSec/IKE/Oakley curve #4 over a 185 bit binary field.
Not suitable for ECDSA.
Questionable extension field!
brainpoolP160r1: RFC 5639 curve over a 160 bit prime field
brainpoolP160t1: RFC 5639 curve over a 160 bit prime field
brainpoolP192r1: RFC 5639 curve over a 192 bit prime field
brainpoolP192t1: RFC 5639 curve over a 192 bit prime field
brainpoolP224r1: RFC 5639 curve over a 224 bit prime field
brainpoolP224t1: RFC 5639 curve over a 224 bit prime field
brainpoolP256r1: RFC 5639 curve over a 256 bit prime field
brainpoolP256t1: RFC 5639 curve over a 256 bit prime field
brainpoolP320r1: RFC 5639 curve over a 320 bit prime field
brainpoolP320t1: RFC 5639 curve over a 320 bit prime field
brainpoolP384r1: RFC 5639 curve over a 384 bit prime field
brainpoolP384t1: RFC 5639 curve over a 384 bit prime field
brainpoolP512r1: RFC 5639 curve over a 512 bit prime field
brainpoolP512t1: RFC 5639 curve over a 512 bit prime field

I only discovered this when trying to build a libpico rpm. The missing curves cause particular problems for Pico, because we use prime192v1 for our implementation of the Sigma-I protocol. Getting around this is awkward, since we don’t have a crypto-negotiation step (maybe there’s a lesson there, although protocol negotiation is also a source of vulnerabilities).
There’s already a bug report covering the missing covers, but given that the situation has persisted since at least 2007 and remains unresolved, it seems unlikely Red Hat’s lawyers will relent any time soon. They’ve added the 256-bit prime field version since this was licensed by the NSA, but the others remain AWOL.
Wikipedia shows the various patents expiring around 2020. Until then, one way to address the problem is to build yourself your own OpenSSL RPM without all of the disabled code. Daniel Pocock produced a nice tutorial back in 2013, but this was for Fedora 19 and OpenSSL 1.0.1e. Things have now moved on and his patch no longer works correctly, so I’ve updated his steps to cover Fedora 25.
Check out my blog post about it if you want to code along.